Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
472 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19098380 | C2 | semidirect |
| 4. C2×#19098378 | C2 | semidirect |
| 6. #23761511 | C2 | semidirect |
| 7. C79×#1385 | C2 | semidirect |
| 170. #1385 | D79 | semidirect |
| 171. C79 | #13006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098839 | 2 |
| #23772008 | 2 |
| C2×#19098380 | 2 |
| C2×#19098378 | 2 |
| #23765029 | 2 |
| #23761511 | 2 |
| C79×#1385 | 2 |
| #13006 | 79 |